Personally I do not use Jetpack for stats but digging into jetpack it seems that the stats are transferred based on the domain name.
Reference:
http://en.forums.wordpress.com/topic/moving-jetpacked-wporg-installation-to-another-site
So technically as long as you have the same mysite.com address it should retain the stats.
As for transferring wordpress over to your own server, I have done this a couple times and the one that seems to work the best for me is this process.
From Old Server:
Export MySQL database
Copy the whole file directory
From new Server:
Install a copy of Wordpress on your server (just to create the DB and file structure)
Empty the newly created MySQL DB and import the database from the Old Server.
Copy/Replace all files from the old server to the new one except for wp-config.php (since it has new credentials)
Lastly I go into wp-admin -> Settings and save the permalinks to have it resetup the .htaccess
Hope this helps.